TSTP Solution File: RNG057+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG057+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:49:44 EDT 2023
% Result : Theorem 14.83s 15.01s
% Output : Proof 14.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG057+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 02:13:35 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 14.83/15.01 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.GPKguJ0bza/cvc5---1.0.5_24211.p...
% 14.83/15.01 ------- get file name : TPTP file name is RNG057+1
% 14.83/15.01 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24211.smt2...
% 14.83/15.01 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 14.83/15.01 --- Run --no-e-matching --full-saturate-quant at 5...
% 14.83/15.01 % SZS status Theorem for RNG057+1
% 14.83/15.01 % SZS output start Proof for RNG057+1
% 14.83/15.01 (
% 14.83/15.01 (let ((_let_1 (tptp.sdtasdt0 tptp.xP tptp.xP))) (let ((_let_2 (not (tptp.sdtlseqdt0 _let_1 tptp.xN)))) (let ((_let_3 (tptp.sdtasdt0 tptp.xC tptp.xD))) (let ((_let_4 (tptp.sdtasdt0 tptp.xH tptp.xH))) (let ((_let_5 (= tptp.xN (tptp.sdtasdt0 _let_4 _let_3)))) (let ((_let_6 (tptp.sdtasdt0 tptp.xE tptp.xE))) (let ((_let_7 (= _let_1 (tptp.sdtasdt0 _let_4 _let_6)))) (let ((_let_8 (tptp.sdtlseqdt0 _let_6 _let_3))) (let ((_let_9 (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS)))) (let ((_let_10 (and (tptp.aScalar0 tptp.xN) _let_9))) (let ((_let_11 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD)))) (let ((_let_12 (and (tptp.aScalar0 tptp.xS) _let_11))) (let ((_let_13 (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH)))) (let ((_let_14 (and (tptp.aScalar0 tptp.xP) _let_13))) (let ((_let_15 (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG)))) (let ((_let_16 (and (tptp.aScalar0 tptp.xR) _let_15))) (let ((_let_17 (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB)))) (let ((_let_18 (and (tptp.aScalar0 tptp.xH) _let_17))) (let ((_let_19 (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB)))) (let ((_let_20 (and (tptp.aScalar0 tptp.xG) _let_19))) (let ((_let_21 (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA)))) (let ((_let_22 (and (tptp.aScalar0 tptp.xF) _let_21))) (let ((_let_23 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq)))) (let ((_let_24 (and (tptp.aScalar0 tptp.xE) _let_23))) (let ((_let_25 (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq)))) (let ((_let_26 (and (tptp.aScalar0 tptp.xD) _let_25))) (let ((_let_27 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp)))) (let ((_let_28 (and (tptp.aScalar0 tptp.xC) _let_27))) (let ((_let_29 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_30 (tptp.sdtlbdtrb0 tptp.xt _let_29))) (let ((_let_31 (and (tptp.aScalar0 tptp.xB) (= tptp.xB _let_30)))) (let ((_let_32 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_33 (tptp.sdtlbdtrb0 tptp.xs _let_32))) (let ((_let_34 (and (tptp.aScalar0 tptp.xA) (= tptp.xA _let_33)))) (let ((_let_35 (tptp.sziznziztdt0 tptp.xt))) (let ((_let_36 (and (tptp.aVector0 tptp.xq) (= tptp.xq _let_35)))) (let ((_let_37 (tptp.sziznziztdt0 tptp.xs))) (let ((_let_38 (and (tptp.aVector0 tptp.xp) (= tptp.xp _let_37)))) (let ((_let_39 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_40 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 tptp.sz0z00 W2) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3))))))) (let ((_let_41 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_42 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_43 (tptp.sdtasdt0 _let_33 _let_30))) (let ((_let_44 (tptp.sdtasasdt0 _let_37 _let_35))) (let ((_let_45 (tptp.sdtasdt0 _let_44 _let_43))) (let ((_let_46 (tptp.sdtasdt0 _let_45 _let_45))) (let ((_let_47 (tptp.sdtasdt0 _let_44 _let_44))) (let ((_let_48 (tptp.sdtasdt0 _let_43 _let_43))) (let ((_let_49 (tptp.sdtasdt0 _let_48 _let_47))) (let ((_let_50 (= _let_49 _let_46))) (let ((_let_51 (tptp.sdtasasdt0 _let_35 _let_35))) (let ((_let_52 (tptp.sdtasasdt0 _let_37 _let_37))) (let ((_let_53 (tptp.sdtasdt0 _let_52 _let_51))) (let ((_let_54 (tptp.sdtasdt0 _let_48 _let_53))) (let ((_let_55 (tptp.sdtasdt0 (tptp.sdtasdt0 _let_52 (tptp.sdtasdt0 _let_30 _let_30)) (tptp.sdtasdt0 (tptp.sdtasdt0 _let_33 _let_33) _let_51)))) (let ((_let_56 (= _let_55 _let_54))) (let ((_let_57 (tptp.sdtlseqdt0 _let_46 _let_55))) (let ((_let_58 (tptp.sdtlseqdt0 _let_49 _let_54))) (let ((_let_59 (1))) (let ((_let_60 (AND_ELIM (ASSUME :args (_let_38)) :args _let_59))) (let ((_let_61 (AND_ELIM (ASSUME :args (_let_36)) :args _let_59))) (let ((_let_62 (AND_ELIM (ASSUME :args (_let_34)) :args _let_59))) (let ((_let_63 (AND_ELIM (ASSUME :args (_let_31)) :args _let_59))) (let ((_let_64 (ASSUME :args (_let_28)))) (let ((_let_65 (EQ_RESOLVE (AND_ELIM _let_64 :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_63 _let_62 _let_61 _let_60) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_26)))) (let ((_let_67 (EQ_RESOLVE (AND_ELIM _let_66 :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (ASSUME :args (_let_24)))) (let ((_let_69 (EQ_RESOLVE (AND_ELIM _let_68 :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_22)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_20)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (ASSUME :args (_let_18)))) (let ((_let_73 (EQ_RESOLVE (AND_ELIM _let_72 :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_16)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_73 _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_14)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_73 _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_12)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_75 _let_74 _let_73 _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (AND_INTRO (EQ_RESOLVE (AND_ELIM (ASSUME :args (_let_10)) :args _let_59) (MACRO_SR_EQ_INTRO (AND_INTRO _let_76 _let_75 _let_74 _let_73 _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) _let_76 _let_75 _let_74 _let_73 _let_71 _let_70 _let_69 _let_67 _let_65 _let_63 _let_62 _let_61 _let_60))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO _let_77 :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO _let_77 :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_77 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (tptp.sdtlseqdt0 _let_47 _let_53))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.sdtlseqdt0 tptp.sz0z00 _let_47))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.sdtlseqdt0 _let_48 _let_48))) (let ((_let_86 (not _let_85))) (let ((_let_87 (tptp.aScalar0 _let_53))) (let ((_let_88 (not _let_87))) (let ((_let_89 (tptp.aScalar0 _let_47))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.aScalar0 _let_48))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_92 _let_90 _let_88 _let_86 _let_84 _let_82 _let_58))) (let ((_let_94 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (tptp.aScalar0 W2)) (not (tptp.aScalar0 W3)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 tptp.sz0z00 W2)) (not (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (or _let_92 _let_85))) (let ((_let_97 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (tptp.aScalar0 _let_43))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_100 _let_100 _let_91))) (let ((_let_102 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (_let_102))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_101))) :args ((or _let_100 _let_91 (not _let_101)))) (EQ_RESOLVE _let_72 (MACRO_SR_EQ_INTRO _let_77 :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_43 _let_43 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_104)) _let_103 :args (_let_101 false _let_102)) :args (_let_91 false _let_99 false _let_101)))) (let ((_let_106 (tptp.aScalar0 _let_44))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_107 _let_89))) (let ((_let_109 (EQ_RESOLVE _let_68 (MACRO_SR_EQ_INTRO _let_77 :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (tptp.aScalar0 _let_51))) (let ((_let_111 (not _let_110))) (let ((_let_112 (tptp.aScalar0 _let_52))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_111 _let_87))) (let ((_let_115 (or _let_107 _let_83))) (let ((_let_116 (forall ((W0 $$unsorted)) (or (not (tptp.aScalar0 W0)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (not _let_58))) (let ((_let_119 (not _let_56))) (let ((_let_120 (not _let_50))) (let ((_let_121 (not _let_57))) (let ((_let_122 (ASSUME :args (_let_58)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_122 _let_78 _let_79 _let_80) :args (_let_50 _let_56 _let_121 _let_58)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_80)) (CONG (SYMM _let_78) (SYMM (SYMM _let_79)) :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_122))) :args (_let_58 _let_50 _let_56 _let_121)) :args ((not (and _let_50 _let_56 _let_121 _let_58)) SB_LITERAL))) (CONG (REFL :args (_let_120)) (REFL :args (_let_119)) (MACRO_SR_PRED_INTRO :args ((= (not _let_121) _let_57))) (REFL :args (_let_118)) :args (or))) :args ((or _let_57 _let_120 _let_119 _let_118))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_93))) :args ((or _let_82 _let_84 _let_88 _let_90 _let_92 _let_86 _let_58 (not _let_93)))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_77 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_107 _let_83 (not _let_115)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_44 QUANTIFIERS_INST_ENUM)) :args (_let_116))) _let_117 :args (_let_115 false _let_116)) :args (_let_83 false _let_106 false _let_115)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_113 _let_111 _let_87 (not _let_114)))) (EQ_RESOLVE _let_64 (MACRO_SR_EQ_INTRO _let_77 :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE _let_66 (MACRO_SR_EQ_INTRO _let_77 :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_52 _let_51 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_104)) _let_103 :args (_let_114 false _let_102)) :args (_let_87 false _let_112 false _let_110 false _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_108))) :args ((or _let_107 _let_89 (not _let_108)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_44 _let_44 QUANTIFIERS_INST_ENUM)) :args _let_104)) _let_103 :args (_let_108 false _let_102)) :args (_let_89 false _let_106 false _let_108)) _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_92 _let_85 (not _let_96)))) _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (_let_48 QUANTIFIERS_INST_ENUM)) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_85 false _let_91 false _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_48 _let_48 _let_47 _let_53 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_58 false _let_81 false _let_83 false _let_87 false _let_89 false _let_91 false _let_85 false _let_93)) _let_80 _let_79 _let_78 :args (false false _let_58 true _let_57 false _let_56 false _let_50)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aNaturalNumber0 W0) (and (tptp.aNaturalNumber0 _let_1) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= W0 (tptp.szszuzczcdt0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) true)) (tptp.aScalar0 tptp.sz0z00) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))) _let_42 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aScalar0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz0z00) W0) (= (tptp.sdtpldt0 tptp.sz0z00 W0) W0) (= (tptp.sdtasdt0 W0 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 W0) tptp.sz0z00) (= (tptp.sdtpldt0 W0 _let_1) tptp.sz0z00) (= (tptp.sdtpldt0 _let_1 W0) tptp.sz0z00) (= (tptp.smndt0 _let_1) W0) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W2 W3)) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W0 W3)) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W2) (tptp.sdtasdt0 W1 W3)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.smndt0 (tptp.sdtasdt0 W0 W1)))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (and (= (tptp.sdtasdt0 W0 (tptp.smndt0 W1)) _let_1) (= (tptp.sdtasdt0 (tptp.smndt0 W0) W1) _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (= (tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1)) (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))) _let_41 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3))))) _let_40 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1)))))) _let_39 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1) (= (tptp.sdtasdt0 W0 W0) (tptp.sdtasdt0 W1 W1))) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (=> (not (= (tptp.aDimensionOf0 W0) tptp.sz00)) (forall ((W1 $$unsorted)) (= (= W1 (tptp.sziznziztdt0 W0)) (and (tptp.aVector0 W1) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 W1)) (tptp.aDimensionOf0 W0)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtlbdtrb0 W1 W2) (tptp.sdtlbdtrb0 W0 W2)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.aDimensionOf0 (tptp.sziznziztdt0 W0)) (tptp.aDimensionOf0 (tptp.sziznziztdt0 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= (tptp.aDimensionOf0 W0) (tptp.aDimensionOf0 W1)) (tptp.aScalar0 (tptp.sdtasasdt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (= _let_1 tptp.sz00)) (= (tptp.sdtasasdt0 W0 W1) tptp.sz0z00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= _let_2 _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))) (and (tptp.aVector0 tptp.xs) (tptp.aVector0 tptp.xt)) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtasasdt0 W0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= _let_2 (tptp.aDimensionOf0 W1)) (=> (tptp.iLess0 _let_2 (tptp.aDimensionOf0 tptp.xs)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_1 _let_1) (tptp.sdtasdt0 (tptp.sdtasasdt0 W0 W0) (tptp.sdtasasdt0 W1 W1))))))))) (= _let_32 _let_29) (not (= _let_32 tptp.sz00)) _let_38 _let_36 _let_34 _let_31 _let_28 _let_26 _let_24 _let_22 _let_20 _let_18 _let_16 _let_14 _let_12 _let_10 _let_8 _let_7 _let_5 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 14.83/15.02 )
% 14.83/15.02 % SZS output end Proof for RNG057+1
% 14.83/15.02 % cvc5---1.0.5 exiting
% 14.83/15.02 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------